On the Long-range Dependence of Fractional Poisson and Negative Binomial Processes

We study the long-range dependence (LRD) of the increments of the fractional Poisson process (FPP), the fractional negative binomial process (FNBP) and the increments of the FNBP. We first point out an error in the proof of Theorem 1 of Biard and Saussereau (2014) and prove that the increments of the FPP has indeed the short-range dependence (SRD) property, when the fractional index $\beta$ satisfies $0<\beta<\frac{1}{3}$. We also establish that the FNBP has the LRD property, while the increments of the FNBP possesses the SRD property.Comment: 17 page

Primordial follicular assembly in humans : revisited

Peer reviewedPreprin

Realizing degree sequences in parallel

A sequence $d$ of integers is a degree sequence if there exists a (simple) graph $G$ such that the components of $d$ are equal to the degrees of the vertices of $G$. The graph $G$ is said to be a realization of $d$. We provide an efficient parallel algorithm to realize $d$. Before our result, it was not known if the problem of realizing $d$ is in $NC$

Performance analysis of microcellization for supporting two mobility classes in cellular wireless networks

We study the call blocking performance obtained by microcellizing a macrocell network. Each macrocell is partitioned into microcells, and some of the channels originally allocated to the macrocell are assigned to the microlayer cells according to a reuse pattern. The arriving calls are classified as fast or slow; fast calls are always assigned only to macrocell channels, whereas for slow calls a microcell channel is first sought. Slow calls may be allowed to overflow to the macrolayer, but may be repacked to vacated microcell channels. Calls can change their mobility class during a conversation. We develop an approximate analysis for computing the slow and fast call blocking probabilities in such a system. We adopt the technique of analyzing an isolated macrocell with the Poisson arrival assumption and then iterating on the stationary analysis of the isolated macrocell to obtain stationary results for the multicell system. Simple, but accurate approximations are developed for analyzing the isolated macrocell and its associated microcells. The analyses based on the approximate isolated cell model are validated against simulations of a multicell model

A simple method of obtaining pure microconidia in Neurospora crassa

In order to examine the nuclear types that may be carried in strains of Neurospora collected from nature, we desired a method of selectively inducing microconidiation in mycelia whereby uninucleate microconidia could be obtained for isolating homokaryotic derivatives. We have devised a simple and highly effective method of obtaining pure microconidia from wild-collected strains as well as from N. crassa 74-OR23-1VA